How to Use the Kelly Criterion for Sports Betting

What Is the Kelly Criterion?

The Kelly Criterion is a mathematical formula that calculates the optimal percentage of your bankroll to wager on a bet, given your edge and the odds. It was developed by John Kelly at Bell Labs in 1956 and has since become the gold standard for bankroll management in investing, gambling, and sports betting.

The core idea: bet more when your edge is large, less when it's small, and nothing when you have no edge. Over time, this strategy maximizes the growth rate of your bankroll while minimizing the risk of ruin.

The Kelly Formula

Kelly % = (b x p - q) / b

Where:

• b = decimal odds - 1 (your net profit per dollar wagered)
• p = true probability of winning
• q = 1 - p (probability of losing)

The result is the fraction of your bankroll you should wager.

Example 1: A Simple Bet

You find a bet at +150 (decimal 2.50) and estimate the true probability of winning is 45%.

• b = 2.50 - 1 = 1.50
• p = 0.45
• q = 0.55

Kelly % = (1.50 x 0.45 - 0.55) / 1.50
Kelly % = (0.675 - 0.55) / 1.50
Kelly % = 0.125 / 1.50
Kelly % = 0.0833 = 8.33%

With a $10,000 bankroll, you'd wager $833.

Example 2: A Smaller Edge

A bet at -110 (decimal 1.91) with a true win probability of 54%.

• b = 1.91 - 1 = 0.91
• p = 0.54
• q = 0.46

Kelly % = (0.91 x 0.54 - 0.46) / 0.91
Kelly % = (0.4914 - 0.46) / 0.91
Kelly % = 0.0314 / 0.91
Kelly % = 0.0345 = 3.45%

With a $10,000 bankroll, you'd wager $345. The smaller edge produces a smaller recommended stake, exactly as it should.

Why Kelly Criterion Works

Maximizes Long-Term Growth

Kelly betting is mathematically proven to produce the highest long-term growth rate of any staking strategy. No flat-staking, percentage-staking, or progressive system can beat it over a large sample.

The key insight: Kelly compounds optimally. When you win, your next bet is larger (because your bankroll grew). When you lose, your next bet is smaller. This natural scaling prevents catastrophic losses while aggressively exploiting edges.

Prevents Overbetting

One of the most common mistakes in sports betting is staking too much on a single bet. Kelly prevents this by tying your stake directly to your edge. A small edge means a small bet, no matter how "confident" you feel.

Prevents Underbetting

Equally, many bettors underbet when they have a genuine edge. Flat-staking $100 on every bet (whether the edge is 1% or 10%) leaves money on the table. Kelly allocates proportionally.

The Problem with Full Kelly

In theory, full Kelly is optimal. In practice, it's extremely volatile. Here's why:

Variance Is Brutal

Full Kelly can produce drawdowns of 50% or more before recovering. For a bettor with a 5% average edge, it's not uncommon to see their bankroll cut in half during a bad streak, even with a winning strategy.

Probability Estimates Are Imperfect

The Kelly formula assumes you know the true probability exactly. In reality, you're estimating it from devigged lines, models, or historical data. If your estimate is off by even a few percentage points, full Kelly can lead to massive overbetting.

Simultaneous Bets

The basic Kelly formula assumes you're betting sequentially, one bet at a time. In practice, you might have 10+ open bets at once. Full Kelly on each one can result in over 100% of your bankroll at risk.

Fractional Kelly: The Practical Solution

Almost every professional bettor uses fractional Kelly, betting a fixed fraction of the full Kelly recommendation. This sacrifices some theoretical growth for dramatically reduced variance.

Half Kelly: The Sweet Spot

Half Kelly is the most popular choice among professionals. You get 75% of the growth rate of full Kelly with dramatically less variance. Your maximum drawdowns are roughly half what full Kelly would produce.

Using our first example (8.33% full Kelly), half Kelly would recommend 4.17% of your bankroll, or $417 on a $10,000 bankroll.

Quarter Kelly: The Conservative Approach

Quarter Kelly is ideal for bettors who:

• Are still building confidence in their probability estimates
• Have a smaller bankroll where large drawdowns would be psychologically difficult
• Want very steady, predictable growth

When Kelly Says Don't Bet

If the Kelly formula returns a negative number, the bet has negative expected value. Don't take it.

Kelly % = (1.50 x 0.35 - 0.65) / 1.50
Kelly % = (0.525 - 0.65) / 1.50
Kelly % = -0.0833

A negative Kelly means the odds aren't in your favor. No staking strategy can overcome a negative edge.

Kelly Criterion with Multiple Simultaneous Bets

When you have multiple bets open at the same time, you need to adjust. The simplest approach:

Method 1: Reduce by Number of Bets

If you typically have n bets open simultaneously, divide your Kelly stake by n. This ensures your total exposure stays within Kelly bounds.

Method 2: Use Fractional Kelly

Using half or quarter Kelly naturally solves the simultaneous bet problem. If you're already betting at 25% Kelly, even 10 concurrent bets only risk about 25% of what full Kelly would on a single bet.

Method 3: Track Total Exposure

Monitor your total outstanding risk at any time. If your combined stakes exceed your full Kelly recommendation for a single bet, you're overexposed.

Common Mistakes

Using Kelly Without an Edge

Kelly is a sizing tool, not an edge-finding tool. If you don't have positive expected value, no amount of clever staking will make you profitable. Find your edge first, then use Kelly to size it.

Overestimating Your Probability

If you think the true probability is 55% but it's actually 51%, full Kelly will recommend roughly double the appropriate stake. This is the primary argument for fractional Kelly: it builds in a margin of safety for estimation errors.

Not Adjusting for Bankroll Changes

Kelly is dynamic. Your stake should change as your bankroll changes. After a winning streak, you bet more. After a losing streak, you bet less. Many bettors set a Kelly stake and never update it, defeating the purpose.

Ignoring Correlation

If you bet on three players from the same team to score, those bets are correlated. Kelly assumes independence between bets. Correlated bets should be treated as a single larger bet for sizing purposes.

Kelly Criterion vs. Flat Staking

Flat staking isn't bad. It's just not optimal. If you don't trust your probability estimates, flat staking 1-2% of your bankroll is a reasonable starting point. As your confidence in your edge assessment grows, transition to fractional Kelly.

Getting Started with Kelly

1. Find your edge by using a +EV scanner or devigging tool to identify bets with positive expected value
2. Estimate true probabilities by devigging sharp lines to get fair odds
3. Start with quarter Kelly and build confidence before increasing
4. Track and review. Monitor your CLV and adjust your Kelly fraction based on results
5. Use a calculator. Don't do Kelly math in your head

The Kelly Criterion is one of the most powerful tools in a bettor's arsenal, but only if you already have an edge. Find the edge first. Then let Kelly tell you how much to bet.